This invention is concerned generally with the application of sampling theory to waveform reconstruction, and more specifically to alias detection in digital oscilloscopes. Aliasing, an inherent problem in single shot analog to digital conversions, is an inaccurate reconstruction of a waveform caused by taking an insufficient number of samples per period of the signal being sampled. This misrepresentation, if not detected, can result in erroneous measurements being made. If detected, the sampling rate may be increased to a rate which enables accurate reconstruction of the original waveshape.
Systems well-known in the prior art were used to prevent Nyquist aliased signals from appearing on the user's display. These systems consisted of a series of switches and filters, which were used to filter out most signals faster than one-half the sampling frequency. The systems required changing the switches to change the filter when the sampling rate was changed. These systems could be cumbersome, expensive, and involved unattractive design trade-offs.
These systems could work well using ideal filters with infinite roll-off. But the practical implementation often fell short of the ideal. If the filter completely filtered out the aliased components, components that were not aliased were also filtered out and this reduced the usefulness of the system.
There were no alias detectors known in the prior art. For aliasing to be detected, the user had to notice irregularities in the reconstruction or display of the waveform, which sometimes didn't exist or appeared to be caused by something else, or the user would have to estimate the sampling rate required for accurate reconstruction from the frequency, which could not be done if the frequency was unknown. If the waveform shifted on the screen, a knowledgeable user might have understood that aliasing was a problem, but also could have attributed the problem to improper triggering. A user unfamiliar with aliasing would be at a loss to understand the problem. If the frequency of the waveform under test had been known, the appropriate sampling rate might have been estimated ahead of time to avoid aliasing. However, if the frequency was not known the user would not be able to estimate an appropriate sampling rate.
Nyquist's theorem states that if greater than two sample points per cycle of a waveform are obtained, then those samples contain enough information to accurately reconstruct the original waveshape. If fewer than two sample points per cycle are captured, then there is insufficient information to reconstruct the original waveshape.